Linv invariant and $G_2$ web space
Takuro Sakamoto, Yasuyoshi Yonezawa
TL;DR
This paper reconstructs the $G_2$ web space using new diagrams and relations, enabling the calculation of $G_2$ quantum link invariants for certain torus links, advancing understanding of quantum invariants.
Contribution
It introduces a new web diagram and relations for $G_2$ web space, facilitating the computation of quantum link invariants and expanding the web calculus framework.
Findings
Reconstructed $G_2$ web space with new diagrams and relations
Defined crossing formulas for $G_2$ R-matrices
Calculated $G_2$ quantum link invariants for some torus links
Abstract
In this paper, we reconstruct Kuperberg's web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the webs, we define crossing formulas corresponding to R-matrices associated to some irreducible representations and calculate quantum link invariant for some torus links.
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